Publication Cover
Stochastics
An International Journal of Probability and Stochastic Processes
Volume 95, 2023 - Issue 1
265
Views
0
CrossRef citations to date
0
Altmetric
Research Article

A contagion process with self-exciting jumps in credit risk applications

ORCID Icon, ORCID Icon & ORCID Icon
Pages 79-98 | Received 20 Oct 2021, Accepted 07 Feb 2022, Published online: 28 Feb 2022

References

  • Y. Aït-Sahalia, J. Cacho-Diaz, and R.J. Laeven, Modeling financial contagion using mutually exciting jump processes, J. Financ. Econ. 117 (2015), pp. 585–606.
  • M. Arnsdorf and I. Halperin, Bslp: Markovian bivariate spread-loss model for portfolio credit derivatives, J. Comput. Finance 12 (2008), pp. 77–107.
  • A. Dassios and H. Zhao, A dynamic contagion process, Adv. Appl. Probab. 43 (2011), pp. 814–846.
  • A. Dassios and H. Zhao, A generalized contagion process with an application to credit risk, Int. J. Theor. Appl. Finance 20 (2017), p. 1750003.
  • M. Davis and V. Lo, Infectious defaults, Quant. Finance 1 (2001), pp. 382–387.
  • D. Duffie and N. Garleanu, Risk and valuation of collateralized debt obligations, Financ. Anal. J. 57 (2001), pp. 41–59.
  • D. Duffie and K.J. Singleton, Modeling term structures of defaultable bonds, Rev. Financ. Stud. 12 (1999), pp. 687–720.
  • E. Errais, K. Giesecke, and L.R. Goldberg, Affine point processes and portfolio credit risk, SIAM J. Financ. Math. 1 (2010), pp. 642–665.
  • D. Filipovic, L. Overbeck, and T. Schmidt, Dynamic CDO term structure modelling, Math. Financ. 21 (2011), pp. 53–71.
  • R. Frey and A.J. McNeil, Dependent defaults in models of portfolio credit risk, J. Risk 6 (2003), pp. 59–92.
  • K. Giesecke, Portfolio credit risk: Top-down vs bottom-up, in Frontiers in Quantitative Finance: Volatility and Credit Risk Modeling, R. Cont, ed., chap. 10, Wiley, New York, 2008, pp. 251–267.
  • A.G. Hawkes, Spectra of some self-exciting and mutually exciting point processes, Biometrika 58 (1971), pp. 83–90.
  • R.A. Jarrow and S.M. Turnbull, Pricing derivatives on financial securities subject to credit risk, J. Finance 50 (1995), pp. 53–85.
  • R.A. Jarrow and F. Yu, Counterparty risk and the pricing of defaultable securities, J. Finance 56 (2001), pp. 1765–1799.
  • M. Kijima and Y. Muromachi, Credit events and the valuation of credit derivatives of basket type, Rev. Deriv. Res. 4 (2000), pp. 55–79.
  • J. Kim, Y.J. Park, and D. Ryu, Hawkes-diffusion process and the conditional probability of defaults in the Eurozone, Phys. A 449 (2016), pp. 301–310.
  • D. Lando, On cox processes and credit risky securities, Rev. Deriv. Res. 2 (1998), pp. 99–120.
  • J.P. Laurent and J. Gregory, Basket default swaps, CDOs and factor copulas, J. Risk 7 (2005), pp. 1.
  • D.X. Li, On default correlation: A copula function approach, J. Fixed Income 9 (2000), pp. 43–54.
  • A. Mortensen, Semi-analytical valuation of basket credit derivatives in intensity-based models, J. Deriv. 13 (2006), pp. 8–26.
  • D. Oakes, The Markovian self-exciting process, J. Appl. Probab. 12 (1975), pp. 69–77.
  • J. Pan and Q. Xiao, A reduced-form model for pricing defaultable bonds and credit default swaps with stochastic recovery, Appl. Stoch. Models Bus. Ind. 32 (2016), pp. 725–739.
  • P. Pasricha and A. Goel, Pricing vulnerable power exchange options in an intensity based framework, J. Comput. Appl. Math. 355 (2019), pp. 106–115.
  • P. Pasricha and D. Selvamuthu, A Markov modulated dynamic contagion process with application to credit risk, J. Stat. Phys. 175 (2019), pp. 495–511.
  • L. Schloegl and D. O'Kane, A note on the large homogeneous portfolio approximation with the student-t copula, Finance Stoch. 9 (2005), pp. 577–584.
  • P.J. Schönbucher, Term structure modelling of defaultable bonds, Rev. Deriv. Res. 2 (1998), pp. 161–192.
  • L. Tchuindjo, Pricing of multi-defaultable bonds with a two-correlated-factor hull–white model, Appl. Math. Finance 14 (2007), pp. 19–39.
  • J.L. Wu and W. Yang, Pricing CDOs tranches in an intensity based model with the mean reversion approach, Math. Comput. Model. 52 (2010), pp. 814–825.
  • J.L. Wu and W. Yang, Valuation of synthetic CDOs with affine jump-diffusion processes involving Lévy stable distributions, Math. Comput. Model. 57 (2013), pp. 570–583.
  • V.F. Zaitsev and A.D. Polyanin, Handbook of Exact Solutions for Ordinary Differential Equations, Chapman and Hall/CRC, Boca Raton, 2002.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.